Free Energy of the Two–Matrix Model/dToda Tau–Function
نویسنده
چکیده
We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the τ function of the dispersionless two–dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal maps of Jordan curves. Finally we provide an integral formula for the free energy of the two-matrix model in the case of arbitrary genus spectral curves.
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تاریخ انتشار 2003